Question

Make a decision about the given claim. Use only the rare event rule, and make subjective estimates to determine whether events are likely. For example, if the claim is that a coin favors heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favors heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).

Claim: The mean pulse rate (in beats per minute) of students in a large math class is greater than 71. A simple random sample of the students has a mean pulse rate of 71.7. Choose the correct answer below.
A. The sample is unusual if the claim is true. The sample is unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim.
B. The sample is unusual if the claim is true. The sample is unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.
C. The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.
D. The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim.

Answer 1

The correct option is (D).

Explanation:

In this case, we need to test whether the mean pulse rate (in beats per minute) of students in a large math class is greater than 71.

The hypothesis can be defined as follows:

H₀: The mean pulse rate of students in a large math class is not greater than 71, i.e. μ ≤ 71.

Hₐ: The mean pulse rate of students in a large math class is greater than 71, i.e. μ > 71.

It is provided that the sample mean pulse rate, of a simple random sample of the students is 71.7.

The sample mean is not very different from the population mean.

So, it cannot be said in confidence that the sample is unusual.

Thus, the correct option is (D).

"The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim."